A Randomized Algorithm for the MaxFS Problem

Abstract

We consider the NP-hard combinatorial optimization problem of finding a feasible subsystem of maximum cardinality among a given set of linear inequalities. In some new and challenging applications in digital broadcasting and in the modelling of protein folding potentials one faces very large MaxFS instances with up to millions of inequalities in thousands of variables. We introduce and analyze a randomized algorithm that is surprisingly successful at solving MaxFS instances that arise in these contexts and exhibit some numerical results.

Raphael Hauser was supported through grant NAL/00720/G from the Nuffield Foundation and through grant GR/M30975 from the Engineering and Physical Sciences Research Council of the UK